void sub(vec_ZZ_pE& x, const vec_ZZ_pE& a, const vec_ZZ_pE& b)
{
long n = a.length();
if (b.length() != n) LogicError("vector sub: dimension mismatch");
x.SetLength(n);
long i;
for (i = 0; i < n; i++)
sub(x[i], a[i], b[i]);
}
void add(vec_ZZ_pE& x, const vec_ZZ_pE& a, const vec_ZZ_pE& b)
{
long n = a.length();
if (b.length() != n) Error("vector add: dimension mismatch");
x.SetLength(n);
long i;
for (i = 0; i < n; i++)
add(x[i], a[i], b[i]);
}
void InnerProduct(ZZ_pE& x, const vec_ZZ_pE& a, const vec_ZZ_pE& b)
{
long n = min(a.length(), b.length());
long i;
ZZ_pX accum, t;
clear(accum);
for (i = 0; i < n; i++) {
mul(t, rep(a[i]), rep(b[i]));
add(accum, accum, t);
}
conv(x, accum);
}
void clear(vec_ZZ_pE& x)
{
long n = x.length();
long i;
for (i = 0; i < n; i++)
clear(x[i]);
}
void negate(vec_ZZ_pE& x, const vec_ZZ_pE& a)
{
long n = a.length();
x.SetLength(n);
long i;
for (i = 0; i < n; i++)
negate(x[i], a[i]);
}
void mul(vec_ZZ_pE& x, const vec_ZZ_pE& a, const ZZ_pE& b_in)
{
ZZ_pE b = b_in;
long n = a.length();
x.SetLength(n);
long i;
for (i = 0; i < n; i++)
mul(x[i], a[i], b);
}
void InnerProduct(ZZ_pE& x, const vec_ZZ_pE& a, const vec_ZZ_pE& b,
long offset)
{
if (offset < 0) LogicError("InnerProduct: negative offset");
if (NTL_OVERFLOW(offset, 1, 0)) ResourceError("InnerProduct: offset too big");
long n = min(a.length(), b.length()+offset);
long i;
ZZ_pX accum, t;
clear(accum);
for (i = offset; i < n; i++) {
mul(t, rep(a[i]), rep(b[i-offset]));
add(accum, accum, t);
}
conv(x, accum);
}
void FindFactors(vec_ZZ_pEX& factors, const ZZ_pEX& f, const ZZ_pEX& g,
const vec_ZZ_pE& roots)
{
long r = roots.length();
factors.SetMaxLength(r);
factors.SetLength(0);
RecFindFactors(factors, f, g, roots, 0, r-1);
}
void mul(vec_ZZ_pE& x, const vec_ZZ_pE& a, long b_in)
{
NTL_ZZ_pRegister(b);
b = b_in;
long n = a.length();
x.SetLength(n);
long i;
for (i = 0; i < n; i++)
mul(x[i], a[i], b);
}
long IsZero(const vec_ZZ_pE& a)
{
long n = a.length();
long i;
for (i = 0; i < n; i++)
if (!IsZero(a[i]))
return 0;
return 1;
}
void IterFindFactors(vec_ZZ_pEX& factors, const ZZ_pEX& f,
const ZZ_pEX& g, const vec_ZZ_pE& roots)
{
long r = roots.length();
long i;
ZZ_pEX h;
factors.SetLength(r);
for (i = 0; i < r; i++) {
sub(h, g, roots[i]);
GCD(factors[i], f, h);
}
}
void VectorCopy(vec_ZZ_pE& x, const vec_ZZ_pE& a, long n)
{
if (n < 0) LogicError("VectorCopy: negative length");
if (NTL_OVERFLOW(n, 1, 0)) ResourceError("overflow in VectorCopy");
long m = min(n, a.length());
x.SetLength(n);
long i;
for (i = 0; i < m; i++)
x[i] = a[i];
for (i = m; i < n; i++)
clear(x[i]);
}
static
void RecFindRoots(vec_ZZ_pE& x, const ZZ_pEX& f)
{
if (deg(f) == 0) return;
if (deg(f) == 1) {
long k = x.length();
x.SetLength(k+1);
negate(x[k], ConstTerm(f));
return;
}
ZZ_pEX h;
ZZ_pEX r;
{
ZZ_pEXModulus F;
build(F, f);
do {
random(r, deg(F));
if (IsOdd(ZZ_pE::cardinality())) {
PowerMod(h, r, RightShift(ZZ_pE::cardinality(), 1), F);
sub(h, h, 1);
}
else {
AbsTraceMap(h, r, F);
}
GCD(h, h, f);
} while (deg(h) <= 0 || deg(h) == deg(f));
}
RecFindRoots(x, h);
div(h, f, h);
RecFindRoots(x, h);
}
static
void mul_aux(vec_ZZ_pE& x, const mat_ZZ_pE& A, const vec_ZZ_pE& b)
{
long n = A.NumRows();
long l = A.NumCols();
if (l != b.length())
Error("matrix mul: dimension mismatch");
x.SetLength(n);
long i, k;
ZZ_pX acc, tmp;
for (i = 1; i <= n; i++) {
clear(acc);
for (k = 1; k <= l; k++) {
mul(tmp, rep(A(i,k)), rep(b(k)));
add(acc, acc, tmp);
}
conv(x(i), acc);
}
}
static
void mul_aux(vec_ZZ_pE& x, const vec_ZZ_pE& a, const mat_ZZ_pE& B)
{
long n = B.NumRows();
long l = B.NumCols();
if (n != a.length())
Error("matrix mul: dimension mismatch");
x.SetLength(l);
long i, k;
ZZ_pX acc, tmp;
for (i = 1; i <= l; i++) {
clear(acc);
for (k = 1; k <= n; k++) {
mul(tmp, rep(a(k)), rep(B(k,i)));
add(acc, acc, tmp);
}
conv(x(i), acc);
}
}
void solve(ZZ_pE& d, vec_ZZ_pE& X,
const mat_ZZ_pE& A, const vec_ZZ_pE& b)
{
long n = A.NumRows();
if (A.NumCols() != n)
Error("solve: nonsquare matrix");
if (b.length() != n)
Error("solve: dimension mismatch");
if (n == 0) {
set(d);
X.SetLength(0);
return;
}
long i, j, k, pos;
ZZ_pX t1, t2;
ZZ_pX *x, *y;
const ZZ_pXModulus& p = ZZ_pE::modulus();
vec_ZZ_pX *M = NTL_NEW_OP vec_ZZ_pX[n];
for (i = 0; i < n; i++) {
M[i].SetLength(n+1);
for (j = 0; j < n; j++) {
M[i][j].rep.SetMaxLength(2*deg(p)-1);
M[i][j] = rep(A[j][i]);
}
M[i][n].rep.SetMaxLength(2*deg(p)-1);
M[i][n] = rep(b[i]);
}
ZZ_pX det;
set(det);
for (k = 0; k < n; k++) {
pos = -1;
for (i = k; i < n; i++) {
rem(t1, M[i][k], p);
M[i][k] = t1;
if (pos == -1 && !IsZero(t1)) {
pos = i;
}
}
if (pos != -1) {
if (k != pos) {
swap(M[pos], M[k]);
negate(det, det);
}
MulMod(det, det, M[k][k], p);
// make M[k, k] == -1 mod p, and make row k reduced
InvMod(t1, M[k][k], p);
negate(t1, t1);
for (j = k+1; j <= n; j++) {
rem(t2, M[k][j], p);
MulMod(M[k][j], t2, t1, p);
}
for (i = k+1; i < n; i++) {
// M[i] = M[i] + M[k]*M[i,k]
t1 = M[i][k]; // this is already reduced
x = M[i].elts() + (k+1);
y = M[k].elts() + (k+1);
for (j = k+1; j <= n; j++, x++, y++) {
// *x = *x + (*y)*t1
mul(t2, *y, t1);
add(*x, *x, t2);
}
}
}
else {
clear(d);
goto done;
}
}
X.SetLength(n);
for (i = n-1; i >= 0; i--) {
clear(t1);
for (j = i+1; j < n; j++) {
mul(t2, rep(X[j]), M[i][j]);
add(t1, t1, t2);
}
sub(t1, t1, M[i][n]);
conv(X[i], t1);
}
conv(d, det);
done:
delete[] M;
}
